Simplify; express your answer in exponential form. Assume $r\neq 0, n\neq 0$. $\dfrac{{r^{4}}}{{(r^{4}n^{3})^{3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${r^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${r^{4} = r^{4}}$ In the denominator, we can use the distributive property of exponents. ${(r^{4}n^{3})^{3} = (r^{4})^{3}(n^{3})^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{r^{4}}}{{(r^{4}n^{3})^{3}}} = \dfrac{{r^{4}}}{{r^{12}n^{9}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{4}}}{{r^{12}n^{9}}} = \dfrac{{r^{4}}}{{r^{12}}} \cdot \dfrac{{1}}{{n^{9}}} = r^{{4} - {12}} \cdot n^{- {9}} = r^{-8}n^{-9}$.